In hitherto known flat keys of this type the cylinder rotor tumbler pins inclined preferably by an angle of 45.degree. to the surface of the key inserted in the key slot, form with the associated key recesses an additional permutation to the conventional 90.degree. lateral permutation formed by the tumbler pins located in perpendicular manner on the key surface and the key recesses belonging thereto. The key recesses follow one another in rows, each set of recesses running in the longitudinal direction of the flat key, each set belonging to one of the various tumbler planes. Thus, the sets of recesses are successively drilled into, or milled from, the two flat sides of the key. As is known in the prior art, it is necessary for this purpose to have a special drilling or milling spindle for each tumbler plane depending upon its slope angle relative to the key surface, i.e., a multiple-spindle machine tool with three main spindles for manufacturing flat keys constructed as turning keys. While such machines admittedly produce optimum slides on the sides of the recesses for the removal of the tumbler pins from the recesses, accompanied by limited space requirements for the recesses on the key shank, their construction is complicated and therefore expensive to produce.